Abstract

A time-domain Legendre spectral-element method is described for full-wave simulation of ocean acoustics models, i.e., coupled fluid-solid problems in unbounded or semi-infinite domains, taking into account shear wave propagation in the ocean bottom. The technique can accommodate range-dependent and depth-dependent wave speed and density, as well as steep ocean floor topography. For truncation of the infinite domain, to efficiently absorb outgoing waves, a fluid-solid complex-frequency-shifted unsplit perfectly matched layer is introduced based on the complex coordinate stretching technique. The complex stretching is rigorously taken into account in the derivation of the fluid-solid matching condition inside the absorbing layer, which has never been done before in the time domain. Two implementations are designed: a convolutional formulation and an auxiliary differential equation formulation because the latter allows for implementation of high-order time schemes, leading to reduced numerical dispersion and dissipation, a topic of importance, in particular, in long-range ocean acoustics simulations. The method is validated for a two dimensional fluid-solid Pekeris waveguide and for a three dimensional seamount model, which shows that the technique is accurate and numerically long-time stable. Compared with widely used paraxial absorbing boundary conditions, the perfectly matched layer is significantly more efficient at absorbing both body waves and interface waves.

We thank Ushnish Basu and Ole Sigmund for fruitful discussions. We also thank two anonymous reviewers for useful comments that improved the manuscript. Part of this work was funded by the Simone and Cino del Duca/Institut de France/French Academy of Sciences Foundation under grant 095164 and by the European “Mont-Blanc: European scalable and power efficient HPC platform based on low-power embedded technology” 288777 project of call FP7-ICT-2011-7. Z.X. also thanks the China Scholarship Council, Key Projects in the National Science & Technology Pillar Program during the 12th Five-year Plan Period (2015BAK17B01), the NSF of the Heilongjiang Province of China (LC201403) and NGSTSP of China (2013zx06002001-09) for financial support, and the continuous support from Professor Liao Zhenpeng. This work was also granted access to the French HPC resources of TGCC under allocations 2014-gen7165 and 2015-gen7165 made by GENCI and of the Aix-Marseille Supercomputing Mesocenter under allocations 14B013 and 15B034.

Article outline:I. INTRODUCTIONII. FORMULATION OF THE WAVE EQUATION IN COUPLED FLUID-SOLID DOMAINSIII. CFS-UPML EQUATIONS FOR FLUID-SOLID DOMAIN TRUNCATIONA. Strong form in the frequency domainB. Strong form in the time domainC. Weak form in the time domainD. Numerical implementationIV. NUMERICAL RESULTSA. 2D elastic Pekeris waveguideB. 3D wave propagation around an elastic seamountV. CONCLUSIONS AND FUTURE WORK